The growth and assembly of a massive galaxy at z∼ 2

We study the stellar mass assembly of the Spiderweb galaxy  (MRC 1138−262)  , a massive   z = 2.2  radio galaxy in a protocluster and the probable progenitor of a brightest cluster galaxy. Nearby protocluster galaxies are identified and their properties are determined by fitting stellar population models to their rest-frame ultraviolet to optical spectral energy distributions. We find that within 150 kpc of the radio galaxy the stellar mass is centrally concentrated in the radio galaxy, yet most of the dust-uncorrected, instantaneous star formation occurs in the surrounding low-mass satellite galaxies. We predict that most of the galaxies within 150 kpc of the radio galaxy will merge with the central radio galaxy by   z = 0  , increasing its stellar mass by up to a factor of ≃2. However, it will take several hundred Myr for the first mergers to occur, by which time the large star formation rates are likely to have exhausted the gas reservoirs in the satellite galaxies. The tidal radii of the satellite galaxies are small, suggesting that stars and gas are being stripped and deposited at distances of tens of kpc from the central radio galaxy. These stripped stars may become intracluster stars or form an extended stellar halo around the radio galaxy, such as those observed around cD galaxies in cluster cores.     

Ram pressure stripping of spiral galaxies in clusters

We use three-dimensional SPH/ N -body simulations to study ram pressure stripping of gas from spiral galaxies orbiting in clusters. We find that the analytic expectation of Gunn & Gott, relating the gravitational restoring force provided by the disc to the ram pressure force, provides a good approximation to the radius at which gas will be stripped from a galaxy. However, at small radii it is also important to consider the potential provided by the bulge component. A spiral galaxy passing through the core of a rich cluster, such as Coma, will have its gaseous disc truncated to ∼4 kpc, thus losing ∼80 per cent of its diffuse gas mass. The time-scale for this to occur is a fraction of a crossing time ∼10⁷ yr. Galaxies orbiting within poorer clusters, or inclined to the direction of motion through the intracluster medium, will lose significantly less gas. We conclude that ram pressure alone is insufficient to account for the rapid and widespread truncation of star formation observed in cluster galaxies, or the morphological transformation of Sabs to S0s that is necessary to explain the Butcher–Oemler effect.     

Dark matter haloes within clusters

We examine the properties of dark matter haloes within a rich galaxy cluster using a high-resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 km s⁻¹ within the cluster virial radius of 2 Mpc (with Hubble constant H ₀ = 50 km s⁻¹ Mpc⁻¹). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well-fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —'galaxy harassment'. Mergers between haloes do not occur inside the cluster virial radius.     

Ram pressure stripping the hot gaseous haloes of galaxies in groups and clusters

We use a large suite of carefully controlled full hydrodynamic simulations to study the ram pressure stripping of the hot gaseous haloes of galaxies as they fall into massive groups and clusters. The sensitivity of the results to the orbit, total galaxy mass, and galaxy structural properties is explored. For typical structural and orbital parameters, we find that ∼30 per cent of the initial hot galactic halo gas can remain in place after 10 Gyr. We propose a physically simple analytic model that describes the stripping seen in the simulations remarkably well. The model is analogous to the original formulation of Gunn & Gott, except that it is appropriate for the case of a spherical (hot) gas distribution (as opposed to a face-on cold disc) and takes into account that stripping is not instantaneous but occurs on a characteristic time-scale. The model reproduces the results of the simulations to within ≈10 per cent at almost all times for all the orbits, mass ratios, and galaxy structural properties we have explored. The one exception involves unlikely systems where the orbit of the galaxy is highly non-radial and its mass exceeds about 10 per cent of the group or cluster into which it is falling (in which case the model underpredicts the stripping following pericentric passage). The proposed model has several interesting applications, including modelling the ram pressure stripping of both observed and cosmologically simulated galaxies and as a way to improve present semi-analytic models of galaxy formation. One immediate consequence is that the colours and morphologies of satellite galaxies in groups and clusters will differ significantly from those predicted with the standard assumption of complete stripping of the hot coronae.     

On the dynamics of the satellite galaxies in NGC 5044

The NGC 5044 galaxy group is dominated by a luminous elliptical galaxy that is surrounded by ∼160 dwarf satellites. The projected number density profile of this dwarf population deviates within ∼1/3 of the virial radius from a projected Navarro, Frenk and White (NFW) profile, which is assumed to approximate the underlying total matter distribution. By means of a semi-analytic model, we demonstrate that the interplay between gravitation, dynamical friction and tidal mass loss and destruction can explain the observed number density profile. We use only two parameters in our models: the total to stellar mass fraction of the satellite haloes and the disruption efficiency. The disruption efficiency is expressed by a minimum radius. If the tidal radius of a galaxy (halo) falls below this radius, it is assumed to become unobservable. The preferred parameters are an initial total to stellar mass fraction of ∼20 and a disruption radius of  4 kpc  . In that model, about 20 per cent of all the satellites are totally disrupted on their orbits within the group environment. Dynamical friction is less important in shaping the inner slope of the number density profile because the reduction in mass by tidal forces lowers the impact of the friction term. The main destruction mechanism is tide. In the preferred model, the total B -band luminosity of all disrupted galaxies is about twice the observed luminosity of the central elliptical galaxy, indicating that a significant fraction of stars are scattered into the intragroup medium. Dwarf galaxy satellites closer to the centre of the NGC 5044 group may exhibit optical evidence of partial tidal disruption. If dynamical friction forces the satellite to merge with the central elliptical, the angular momentum of the satellite tends to be removed at the apocentre passage. Afterwards, the satellite drops radially towards the centre.     

The evolution of substructure – III. The outskirts of clusters

We present an investigation of satellite galaxies in the outskirts of galaxy clusters taken from a series of high-resolution N -body simulations. We focus on the so-called backsplash population, i.e. satellite galaxies that once were inside the virial radius of the host but now reside beyond it. We find that this population is significant in number and needs to be appreciated when interpreting the various galaxy morphology environmental relationships and decoupling the degeneracy between nature and nurture. Specifically, we find that approximately half of the galaxies with current cluster-centric distance in the interval 1–2 virial radii of the host are backsplash galaxies that once penetrated deep into the cluster potential, with 90 per cent of these entering to within 50 per cent of the virial radius. These galaxies have undergone significant tidal disruption, losing on average 40 per cent of their mass. This results in a mass function for the backsplash population different from those galaxies infalling for the first time. We further show that these two populations are kinematically distinct and should be observable within existent spectroscopic surveys.     

The concentration–velocity dispersion relation in galaxy groups

Based on results from cold dark matter N -body simulations, we develop a dynamical model for the evolution of subhaloes within group-sized host haloes. Only subhaloes more massive than 5 × 10⁸ M_⊙ are considered, because they are massive enough to possibly host luminous galaxies. On their orbits within a growing host potential the subhaloes are subject to tidal stripping and dynamical friction. At the present time  ( z = 0)  , all model hosts have equal mass  ( M _vir= 3.9 × 10¹³ M_⊙)  but different concentrations associated with different formation times. We investigate the variation of subhalo (or satellite galaxy) velocity dispersion with host concentration and/or formation time. In agreement with the Jeans equation, the velocity dispersion of subhaloes increases with the host concentration. Between concentrations of ∼5 and ∼20, the subhalo velocity dispersions increase by a factor of ∼1.25. By applying a simplified tidal disruption criterion, that is, rejection of all subhaloes with a tidal truncation radius below 3  kpc at   z = 0  , the central velocity dispersion of the 'surviving' subhalo sample increases substantially for all concentrations. The enhanced central velocity dispersions in the surviving subhalo samples are caused by a lack of slow tangential motions. Additionally, we present a fitting formula for the anisotropy parameter which does not depend on concentration if the group-centric distances are scaled by r _s, the characteristic radius of the Navarro, Frenk & White profile. Since the expected loss of subhaloes and galaxies due to tidal disruption increases the velocity dispersion of surviving galaxies, the observed galaxy velocity dispersion can substantially overestimate the virial mass.     

Active galactic nuclei and the minor merger hypothesis

We have investigated the dynamics of the merging process in the minor merger hypothesis for active galactic nuclei. We find that for a satellite galaxy to be able to merge directly with the nucleus of the host galaxy (for example, to give rise to the compact dust discs which are seen in early-type active galaxies), the initial orbit of the satellite is required to be well aimed. For the case of the host galaxy being a disc galaxy, if the initial orbits of the satellites are randomly oriented with respect to the host galaxy, then the orbits of those which reach the host nuclear regions in a reasonable time are also fairly randomly oriented once they reach the nucleus. We note that this result might be able to provide an explanation of why the jet directions in the nuclei of Seyfert galaxies are apparently unrelated to the plane of the galaxy discs.     

Galactic halo cusp–core: tidal compression in mergers

We explain in simple terms how the build-up of dark haloes by merging compact satellites, as in the cold dark matter (CDM) cosmology, inevitably leads to an inner cusp of density profile  ρ∝ r ^−α  with  α≳ 1  , as seen in cosmological N -body simulations. A flatter halo core with  α < 1  exerts on the satellites tidal compression in all directions, which prevents the deposit of stripped satellite material in the core region. This makes the satellite orbits decay from the radius where  α∼ 1  to the halo centre with no local tidal mass transfer, and thus causes a rapid steepening of the inner profile to  α > 1  . These tidal effects, the resultant steepening of the profile to a cusp, and the stability of this cusp to tandem mergers with compact satellites are demonstrated using N -body simulations. The transition at  α∼ 1  is then addressed using toy models in the limiting cases of impulse and adiabatic approximations and using tidal radii for satellites on radial and circular orbits. In an associated paper, we address the subsequent slow convergence from either side to an asymptotic stable cusp with  α≳ 1  . Our analysis thus implies that an inner cusp is enforced when small haloes are typically more compact than larger haloes, as in the CDM scenario, such that enough satellite material makes it intact into the inner halo and is deposited there. We conclude that a necessary condition for maintaining a flat core, as indicated by observations, is that the inner regions of the CDM satellite haloes be puffed up by about 50 per cent such that when they merge into a larger halo they would be disrupted outside the halo core. This puffing up could be due to baryonic feedback processes in small haloes, which may be stimulated by the tidal compression in the halo cores.     

Dynamical friction and galaxy merging time-scales

The time-scale for galaxies within merging dark matter haloes to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging time-scales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies and the statistical properties of satellite galaxies within dark matter haloes. In this paper, we study the merging time-scales of extended dark matter haloes using N -body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging time-scales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for M _sat/ M _host≈ 0.1 and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of ∼3.3 for M _sat/ M _host≈ 0.01. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the time-scale for an extended satellite to sink from the virial radius of a host halo down to the halo's centre for a wide range of M _sat/ M _host and orbits. Including a central bulge in each galaxy changes the merging time-scale by ≲10 per cent. To highlight one concrete application of our results, we show that merging time-scales often used in the literature overestimate the growth of stellar mass by satellite accretion by ≈40 per cent, with the extra mass gained in low mass ratio mergers.     

Resolving the timing problem of the globular clusters orbiting the Fornax dwarf galaxy

We re-investigate the old problem of the survival of the five globular clusters (GCs) orbiting the Fornax dwarf galaxy in both standard and modified Newtonian dynamics (MOND). For the first time in the history of the topic, we use accurate mass models for the Fornax dwarf, obtained through Jeans modelling of the recently published line-of-sight (LOS) velocity dispersion data, and we are also not resigned to circular orbits for the GCs. Previously conceived problems stem from fixing the starting distances of the globulars to be less than half the tidal radius. We relax this constraint since there is absolutely no evidence for it and show that the dark matter (DM) paradigm, with either cusped or cored DM profiles, has no trouble sustaining the orbits of the two least massive GCs for a Hubble time almost regardless of their initial distance from Fornax. The three most massive globulars can remain in orbit as long as their starting distances are marginally outside the tidal radius. The outlook for MOND is also not nearly as bleak as previously reported. Although dynamical friction (DF) inside the tidal radius is far stronger in MOND, outside DF is negligible due to the absence of stars. This allows highly radial orbits to survive, but more importantly circular orbits at distances more than 85 per cent of Fornax's tidal radius to survive indefinitely. The probability of the GCs being on circular orbits at this distance compared with their current projected distances is discussed and shown to be plausible. Finally, if we ignore the presence of the most massive globular (giving it a large LOS distance), we demonstrate that the remaining four globulars can survive within the tidal radius for the Hubble time with perfectly sensible orbits.     

The unusual distribution of molecular gas and star formation in Arp 140

We investigate the atomic and molecular interstellar medium and star formation of NGC 275, the late-type spiral galaxy in Arp 140, which is interacting with NGC 274, an early-type system. The atomic gas (H  i ) observations reveal a tidal tail from NGC 275 which extends many optical radii beyond the interacting pair. The H  i morphology implies a prograde encounter between the galaxy pair approximately ∼1.5 × 10⁸ yr ago. The Hα emission from NGC 275 indicates clumpy irregular star formation, clumpiness which is mirrored by the underlying mass distribution as traced by the K _s-band emission. The molecular gas distribution is striking in its anticorrelation with the H  ii regions. Despite the evolved nature of NGC 275's interaction and its barred potential, neither the molecular gas nor the star formation is centrally concentrated. We suggest that this structure results from stochastic star formation leading to preferential consumption of the gas in certain regions of the galaxy. In contrast to the often-assumed picture of interacting galaxies, NGC 275, which appears to be close to merger, does not display enhanced or centrally concentrated star formation. If the eventual merger is to lead to a significant burst of star formation it must be preceded by a significant conversion of atomic to molecular gas as at the current rate of star formation all the molecular gas will be exhausted by the time the merger is complete.     

Ram pressure stripping of disc galaxies orbiting in clusters – I. Mass and radius of the remaining gas disc

We present the first 3D hydrodynamical simulations of ram pressure stripping of a disc galaxy orbiting in a galaxy cluster. Along the orbit, the ram pressure that this galaxy experiences varies with time. In this paper, we focus on the evolution of the radius and mass of the remaining gas disc, and compare it with the classical analytical estimate proposed by Gunn & Gott. We find that this simple estimate works well in predicting the evolution of the radius of the remaining gas disc. Only if the ram pressure increases faster than the stripping time-scale, the disc radius remains larger than predicted. However, orbits with such short ram pressure peaks are unlikely to occur in other than compact clusters. Unlike the radius evolution, the mass-loss history for the galaxy is not accurately described by the analytical estimate. Generally, in the simulations the galaxy loses its gas more slowly than predicted.     

The pendulum dilemma of fish orbits

The shape of a galaxy is constrained both by mechanisms of formation (dissipational versus dissipationless) and by the available orbit families (the shape and amount of regular and stochastic orbits). It is shown that, despite the often very flattened shapes of banana and fish orbits, these boxlet orbits generally do not fit a triaxial galaxy in detail because, similar to loop orbits, they spend too little time at the major axis of the model density distribution. This constraint from the shape of fish orbits is relaxed at (large) radii where the density profile of a galaxy is steep.     

The dynamical evolution of stellar superclusters

Recent images taken with the Hubble Space Telescope ( HST ) of the interacting disc galaxies NGC 4038/4039 (the Antennae) reveal clusters of many dozens and possibly hundreds of young compact massive star clusters within projected regions spanning about 100 to 500 pc. It is shown here that a large fraction of the individual star clusters merge within a few tens to a hundred Myr. Bound stellar systems with radii of a few hundred parsecs, masses ≲ 10⁹ M⊙ and relaxation times of 10¹¹ − 10¹² yr may form from these. These spheroidal dwarf galaxies contain old stars from the pre-merger galaxy and much younger stars formed in the massive star clusters, and possibly from later gas accretion events. The possibility that star formation in the outer regions of gas-rich tidal tails may also lead to superclusters is raised. The mass-to-light ratio of these objects is small, because they contain an insignificant amount of dark matter. After many hundred Myr such systems may resemble dwarf spheroidal satellite galaxies with large apparent mass-to-light ratios, if tidal shaping is important.     

Dark matter subhaloes in numerical simulations

We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10¹¹ to  10¹⁴ M_⊙  at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation  d n /d v = (1/8)( v _cmax/ v _cmax,host)⁻⁴  . Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for   r ≳ 0.3 r _vir  , where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of   P ∝ kⁿ   , and demonstrate that a steeper spectral index, n , results in significantly less substructure.     

Modelling the dynamical evolution of the Bootes dwarf spheroidal galaxy

We investigate a wide range of possible evolutionary histories for the recently discovered Bootes dwarf spheroidal galaxy, a Milky Way satellite. By means of N -body simulations, we follow the evolution of possible progenitor galaxies of Bootes for a variety of orbits in the gravitational potential of the Milky Way. The progenitors considered cover the range from dark matter-free star clusters to massive, dark matter-dominated outcomes of cosmological simulations. For each type of progenitor and orbit, we compare the observable properties of the remnant after 10 Gyr with those of Bootes observed today. Our study suggests that the progenitor of Bootes must have been, and remains now, dark matter-dominated. In general, our models are unable to reproduce the observed high velocity dispersion in Bootes without dark matter. Our models do not support time-dependent tidal effects as a mechanism able to inflate significantly the internal velocity dispersion. As none of our initially spherical models is able to reproduce the elongation of Bootes, our results suggest that the progenitor of Bootes may have had some intrinsic flattening. Although the focus of this paper is the Bootes dwarf spheroidal, these models may be of general relevance to understanding the structure, stability and dark matter content of all dwarf spheroidal galaxies.     

A minor-merger model for NGC 7479

The overall morphology of the barred spiral galaxy NGC 7479 is modelled in numerical simulations of a minor merger. Special attention is paid to the morphology and velocity field of the asymmetric spiral structure and the strong stellar bar. The mass of the satellite galaxy is 1/10 of the mass of the primary disc, or 1/30 of the total mass of the primary. The satellite is placed initially in a circular prograde orbit at six disc scalelengths from the centre of the primary. We follow the evolution of the merger until the secondary galaxy reaches the nuclear region of the primary. A comparison between the modelled and observed morphologies of the stellar and the ionized and neutral gas distributions and velocity fields supports the hypothesis that the transient look of NGC 7479 is a result of a minor merger. We vary several of the initial parameters of the merger and discuss their effects on the resulting morphology. The merging satellite galaxy is likely to lie within the bar of NGC 7479. We identify a possible candidate in the observational data. We discuss briefly the most probable future evolution of NGC 7479 in the light of our minor-merger simulations, and conclude that NGC 7479 is likely to evolve toward an earlier Hubble type.     

Ram-pressure stripping of disc galaxies orbiting in clusters – II. Galactic wakes

We present 3D hydrodynamical simulations of ram-pressure stripping of a disc galaxy orbiting in a galaxy cluster. In this paper, we focus on the properties of the galaxies' tails of stripped gas. The galactic wakes show a flaring width, where the flaring angle depends on the gas disc's cross-section with respect to the galaxy's direction of motion. The velocity in the wakes shows a significant turbulent component of a few     . The stripped gas is deposited in the cluster rather locally, i.e. within     from where it was stripped. We demonstrate that the most important quantity governing the tail density, length and gas mass distribution along the orbit is the galaxy's mass-loss per orbital length. This in turn depends on the ram pressure as well as the galaxy's orbital velocity.
For a sensitivity limit of     in projected gas density, we find typical tail lengths of     . Such long tails are seen even at large distances (0.5 to     ) from the cluster centre. At this sensitivity limit, the tails show little flaring, but a width similar to the gas disc's size.
Morphologically, we find good agreement with the H  i tails observed in the Virgo cluster by Chung et al. 2007 . However, the observed tails show a much smaller velocity width than predicted from the simulation. The few known X-ray and Hα tails are generally much narrower and much straighter than the tails in our simulations. Thus, additional physics like a viscous intracluster medium (ICM), the influence of cooling and tidal effects may be needed to explain the details of the observations.
We discuss the hydrodynamical drag as a heat source for the ICM but conclude that it is not likely to play an important role, especially not in stopping cooling flows.     

An Analytic Model of Galactic Winds and Mass Outflows

Galactic winds and mass outflows are observed both in nearby starburst galaxies and in high-redshift star-forming galaxies. We develop a simple analytic model to understand the observed superwind phenomenon with a discussion of the model uncertainties. Our model is built upon the model of McKee & Ostriker for the interstellar medium. It allows one to predict how properties of a superwind, such as wind velocity and mass outflow rate, are related to properties of its starforming host galaxy, such as size, gas density and star formation rate. The model predicts a threshold of star formation rate density for the generation of observable galactic winds. Galaxies with more concentrated star formation activities produce superwinds with higher velocities. The predicted mass outflow rates are comparable to (or slightly larger than) the corresponding star formation rates. We apply our model to both local starburst galaxies and high-redshift Lyman break galaxies, and find its predictions to be in good agreement with current observations. Our model is simple and so can be easily incorporated into numerical simulations and semi-analytical models of galaxy formation.